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NEET 1995 (AIPMT) · Potential Energy & Equilibrium

Potential Energy & Equilibrium question from NEET 1995 (AIPMT)

Q16NEET 1995 · AIPMTMedium

Potential Energy & Equilibrium

The potential energy between two atoms, in a molecule, is given by $U(x) = \frac{a}{x^{12}} - \frac{b}{x^6}$ where $a$ and $b$ are positive constants and $x$ is the distance between the atoms. The atom is in stable equilibrium, when

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Answer: (a)

$\frac{dU}{dx} = -\frac{12a}{x^{13}} + \frac{6b}{x^7} = 0$
$x^6 = \frac{2a}{b}$ (this is a minimum of $U$ , so stable)
So the answer is (a) $x = \left(\frac{2a}{b}\right)^{1/6}$ .

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